Statistical Multimode Resonant Annihilation of Positrons on Molecules*

Annihilation at positron energies in the range of the molecular vibrational modes is dominated by large-amplitude vibrational Feshbach resonances (VFR) in which the positron attaches to the molecule.\footnote{G. F. Gribakin, J. A. Young, C. M. Surko, Rev. Mod. Phys. {\bf 82}, 2557 (2010).} In small molecules, there is a quantitative description of the annihilation rates, $Z_{\rm eff}$, due to the VFR.\footnote{G. F. Gribakin, C. M. R. Lee, Phys. Rev. Lett. {\bf 97}, 193201 (2006).} Here we focus on a broad spectrum of enhanced annihilation that is observed in the spectra of many, if not most, molecules.\footnote{A. C. L. Jones, et al., Phys. Rev. Lett., in press (2012).} This spectral component, for example, dominates the spectra in small molecules with relatively large binding energies, such as CCl$_4$ and CBr$_4$. A model that assumes excitation and escape from a statistically complete ensemble of multimode vibrations is presented\footnote{G. F. Gribakin, C. M. R. Lee, European Phys. J. D {\bf 51}, 51 (2009).} that reproduces key features of the data. Related issues of intramolecular vibrational redistribution (IVR), and the effects of escape channels on the primary VFRs will also be discussed.